The present invention relates to an apparatus for measuring 6-degree-of-freedom motions of a rigid body by using a three-facet reflector wherein the measurement of the 6-degree-of-freedom displacements of an object, particularly an object in motion with a high-speed, can be made with ease and with accuracy, and specially the measuring precision is excellent.
Generally, there are various ways for expressing the position and orientation of a body situated in a three dimensional space.
In one of widely used methods, the position is expressed as a position vector on rectangular coordinate system for three dimensional space and the orientation is expressed by means of Euler""s angle expression, in which the rotated angle for an object relative to the x, y and z axis of a reference coordinate system is expressed as xcex3, xcex2 and xcex1 respectively, the rotated angles being called as the roll, pitch and yaw.
Referring to FIG. 1, which shows the rectangular coordinate as defined in the three dimensional space, the position and orientation of an arbitrary object for which measurement is to be taken and which moves with 6-degree-of freedoms are illustrated. The coordinate system Ow is the reference coordinate system to express the motion of an object 1. For a portion of the object 1 in the drawing, the coordinate systems Ow and Os are defined. The coordinate system Os is the coordinate system fixed on the rigid body and moving integrally with the object 1.
Further, the coordinate system Owxe2x80x2 maintains the same orientation as the reference coordinate system Ow and shares the origin with the coordinate system Os. In the drawing, the vector             T      w        →    =            [                                                  t              x                                                          t              y                                                          t              z                                          ]        T  
is the position vector for expressing the position of the object 1 defined by the coordinate system Os. Further, the equation:                                           T            s            w                    =                      [                                                                                c                    ⁢                                          xe2x80x83                                        ⁢                    α                    ⁢                                          xe2x80x83                                        ⁢                    c                    ⁢                                          xe2x80x83                                        ⁢                    β                                                                                                              c                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      β                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      γ                                        -                                          s                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      c                      ⁢                                              xe2x80x83                                            ⁢                      γ                                                                                                                                  c                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      β                      ⁢                                              xe2x80x83                                            ⁢                      c                      ⁢                                              xe2x80x83                                            ⁢                      γ                                        +                                          s                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      γ                                                                                                            t                    x                                                                                                                    s                    ⁢                                          xe2x80x83                                        ⁢                    α                    ⁢                                          xe2x80x83                                        ⁢                    c                    ⁢                                          xe2x80x83                                        ⁢                    β                                                                                                              s                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      β                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      γ                                        +                                          c                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      c                      ⁢                                              xe2x80x83                                            ⁢                      γ                                                                                                                                  s                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      β                      ⁢                                              xe2x80x83                                            ⁢                      c                      ⁢                                              xe2x80x83                                            ⁢                      γ                                        -                                          c                      ⁢                                              xe2x80x83                                            ⁢                      α                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      γ                                                                                                            t                    y                                                                                                                                          -                      s                                        ⁢                                          xe2x80x83                                        ⁢                    β                                                                                        c                    ⁢                                          xe2x80x83                                        ⁢                    β                    ⁢                                          xe2x80x83                                        ⁢                    s                    ⁢                                          xe2x80x83                                        ⁢                    γ                                                                                        c                    ⁢                                          xe2x80x83                                        ⁢                    β                    ⁢                                          xe2x80x83                                        ⁢                    c                    ⁢                                          xe2x80x83                                        ⁢                    γ                                                                                        t                    z                                                                                                0                                                  0                                                  0                                                  1                                                      ]                          ,                            (                  Equation          ⁢                      xe2x80x83                    ⁢          1                )            
wherein stand for and other abridgements have the similar meanings, is the matrix defined by tx, ty, tz, xcex3, xcex2 and xcex1, which expresses the position and orientation of the coordinate system Os moved relative to the reference coordinate Ow. As the coordinate system Os is fixed to the object 1, this matrix can be used to show the position and orientation of the object.
As described above, the determination of the position and orientation of an object in the three dimensional space may be regarded as the problem of determining the 6 values for tx, ty, tz, xcex3, xcex2 and xcex1.
The three-facet reflector used for the measuring apparatus in the present invention was initially suggested in a patent application (Korean patent application No. 99-00977) previously filed. The disclosure in the patent application was intended to determine six-degree-of-freedom motions by attaching a three-facet reflector on the slider of a hard disk drive (HDD). However, while a laser beam was needed to enter the apex of the three-facet reflector for the given purpose, a specific method therefor was not proposed in the disclosure.
Further, the mathematical equations proposed there were derived on the base of the hypothesis that the apex of a three-facet reflector and the laser light spots formed on three position-sensitive detectors form the same one plane. As the hypothesis is not precise in view of the fact, however, the equations can not be applied to the practice. Therefore, that exclusive patent application is not sufficient to achieve the goal.
There is also known a method for measuring six-degree-of-freedom displacements of an object (Korean patent application No. 00-24654) by using the three-facet reflector as proposed in the above-described patent. The arrangement of the apparatuses as proposed in that patent is shown in FIG. 2. On the object, a mirror in the form of a trigonal pyramid as the three-facet reflector 110 is mounted. The three-facet reflector 110 is supplied with a laser beam at its top apex so as to produce three branches of reflected beams, which are detected by three laser beam position-sensitive detectors PSD""s 121, 122 and 123. The position-sensitive detectors 121, 122 and 123 comprise ordinary sensor elements for outputting the locations of centroids for incident laser beams in the form of voltage signal, so that the coordinates of sets of three positions from three position-sensitive detectors 121, 122 and 123 may be used to determine the six-degree-of-freedom displacements tx, ty, tz, xcex3, xcex2 and xcex1 of the three-facet reflector 110. As indicated in the drawing, the laser source follows with two degrees of freedom, as the three-facet reflector 110 makes movement. In order to follow the movement of three-facet reflector 110, the two-degree-of-freedom position of the light source is controlled, so that the intensity of laser beam incident to the three position-sensitive detectors 121, 122 and 123 may be maintained the same, by comparing the intensity of laser beam incident to the respective position-sensitive detectors 121, 122 and 123. This invention is pertinent to the application filed by the present inventors, which realized the laser-tracing method not embodied in the previous patent application (No. 99-00977). However, this method is still insufficient to follow high-speed movements.
FIG. 3 shows the arrangement of a special apparatus as disclosed in Korean patent application No.00-24653, which functions to determine six-degree-of-freedom movements of a HDD slider based on the principle disclosed in Korean patent application No.00-24654. Arms of a two-stage swing arm 140 run parallel to each other and connected to a pivot 14 at the rear end, so that the two-stage swing arm 140 can rotate around the axis of the pivot 14. The lower arm member includes an E-block 16, suspension 18 and flexure piece 19, to the underside of which piece a slider 20 is fixed. The actuator for driving the slider 20 in the form of a voice coil motor(VCM) 12 is disposed on the rear part of the two-stage swing arm 140. The upper arm member of the swing arm 140 is composed of a rigid body resisting an elastic deformation. A three-facet reflector 110 is fixed on the upper side of the slider 20. Right above the apex of the three-facet reflector 110 there is formed a light permeating hole 143 on the leading edge of the upper arm member, while the first reflector 151 and the second reflector 152 are fixed on the top face of the upper arm member of the swing arm 140. A laser beam which has passed the first and second reflectors 151 and 152 arrives at the three-facet reflector 110 through the hole 143 and then the ray reflected thereon is projected to three position-sensitive detectors 121, 122 and 123. In this invention, a two stage swing arm is proposed, so that the laser beam may be projected constantly in the apex of a three-facet reflector which moves together with the HDD slider, because existing ordinary laser-tracing apparatuses were impossible to make a precise tracing due to the high-speed motion of the HDD slider.
As described above, in the method for determining six-degree-of-freedom variables by using a three-facet reflector, a method by which a laser beam can be precisely projected to the apex of the three-facet reflector by tracing precisely the movement of the three-facet reflector has been recognized as an very important issue.
The present invention modified the conventional principle of the measurement of six-degree-of-freedom motions as applied to a three-facet reflector in order to resolve the problems associated with laser tracing in the existing art.
Thus the object of the invention is to provide an apparatus for measuring six-degree-of-freedom motions of an object by using a three-facet reflector wherein a mechanical tracing mechanism is not needed due to the unnecessity of tracing the laser and so measurement of a high-speed movement is possible due to the independence of a mechanical speed restriction.
The object as described above is achieved according to the invention by an apparatus for measuring six-degree-of-freedom motions by using three-facet reflector, the six-degree-of-freedom motions of an object being measured by using the laser beam proceeding from a laser light source, comprising: a three-facet reflector in the form of a trigonal pyramid, the three-facet reflector being fixed on the object for measurement and able to reflect the laser beam in three directions; three position-sensitive detectors for measuring the position and intensity of the laser light points formed on their surfaces, with the movement of the three-facet reflector, and then providing output signals; and a controlling section for analyzing six-degree-of-freedom motions of the three-facet reflector by using the position and intensity of the laser light points output from the three position-sensitive detectors.
Preferably, the range of movement for the three-facet reflector lies within the area irradiated by the laser beam.
Also, according to a feature of the invention, a reflector may comprise more than 3 facets and the same number of position detectors should be used.